The temperature measured in relation to absolute zero using the Kelvin scale is known as absolute temperature.

Temperature is defined as the degree of hotness of a body. It is also defined as the property which determines whether a body is in equilibrium or not with the surroundings.

Charles's law is otherwise called as the law of volume. It states that, when the pressure of gas is kept constant, the volume of the gas is directly proportional to the temperature of the gas.
\(\mathrm{V} \propto {T}\)

When the temperature of a gas is kept constant, the volume of a fixed mass of  gas is inversely proportional to its pressure. \(\mathrm{P} \alpha \frac{1}{\mathrm{~V}}\)

(i) The ratio of increase in volume of the body per degree rise in temperature to its unit volume is called as co-efficient of cubical expansion.
(ii) SI unit is K^-1.
(iii) Co - efficient of cubical expansion can be expressed as \(\frac{\Delta V}{V_{o}}=\alpha_{v} \Delta T\)

Statement of Boyle's law:
When the temperature of a gas is kept constant, the volume of a fixed mass of gas is inversely proportional to its pressure.
∴ P α 1/V

In other words, for an invariable mass of a perfect gas, at constant temperature, the product of pressure and volume is a constant.
Pressure x Volume = constant
PV = constant

Cubical expansion:
(i) If there is an increase in the volume of a solid body due to heating, then the expansion is called cubical or volumetric expansion.
(ii) As in the cases of linear and areal expansion, cubical expansion is also expressed in terms of coefficient of cubical expansion. The ratio of increase in volume of the body per degree rise in temperature to its unit volume is called coefficient of cubical expansion. This is also measured in K^-1.

(iii) The equation relating to the change in volume to the change in temperature is given below:
\(\frac { \triangle V }{ { V }_{ 0 } } \) = α_v ΔT
ΔV - Change in volume
V₀ - Original volume
ΔT - Change in temperature
α_v - Coefficient of cubical expansion.

(i) When heat energy is supplied to a body, there can be an increase in the dimension of the object. This change in the dimension due to rise in temperature is called thermal expansion of the object.
(ii) The expansion of liquids (eg. mercury) can be seen when a thermometer is placed in warm water. All forms of matter (solid, liquid and gas) undergo expansion on heating.
(iii) When a solid is heated, the atoms gain energy and vibrate more vigorously. This results in the expansion of the solid.
(iv) The different types of expansion of solid are
i) Linear expansion
ii) Superficial expansion
iii) Cubical expansion
(v) When heated, the atoms in a liquid or gas gain energy and are forced further apart. The extent of expansion varies from substance to substance. For a given rise in temperature, a liquid will have more expansion than a solid and a gaseous substance has the highest expansion when compared with the other two.

Change in volume \((\Delta V)=0.3-0.25 =0.05\mathrm{~m}^{3}\)
Original volume \(\left(V_{0}\right)=0.3 \mathrm{~m}^{3}\)
Change in Temperature \(\Delta \mathrm{T}=50 \mathrm{~K}\)
\(a_{\mathrm{V}} =?  \)
\(\frac{\Delta V}{V_{0}} =a_{\mathrm{V}} \Delta \mathrm{T}\)
\(a_{\mathrm{V}} =\frac{0.05}{0.3 \times 50}=\frac{0.05}{15}=0.0033 \mathrm{~K}^{-1}\)
Co-efficient of cubical expansion of Zinc bar 0.0033

Area of copper rod,   A_o = 10 m²
Changes of Area of cross section,
Initial temperature \(\Delta \mathrm{A} =11 -10 =1 \mathrm{~m}^{2}  \)
\(\mathrm{~T}_{1} =90 \mathrm{~K}  \)
\(a_{\mathrm{A}} =0.0021 / \mathrm{K}  \)
\(\mathrm{T}_{2} =?  \)
\(\frac{\Delta A}{A_{0}} =a_{\mathrm{A}} \Delta \mathrm{T}  \)
\(\frac{1 }{10 } =0.0021\left[\mathrm{~T}_{2}-90\right]  \)
\(0.1 =0.0021\left[\mathrm{~T}_{2}-90\right]=\frac{0.1}{0.0021}+90=\mathrm{T}_{2}  \)
\(\mathrm{~T}_{2} =137.61 \mathrm{~K}\)
So the final temperature of a copper rod is 137.61 K

Aim:
To measure real and apparent expansion of liquid.
Apparatus Required:
a) Round bottomed flask, a narrow glass tube with a scale, burner.
Procedure:
b) The liquid whose real and apparent expansion is to be determined is poured in a container up to a level.
c) Mark this level as L₁.
d) Now, heat the container and the liquid using a burner.
e) Initially, the container receives the thermal energy and it expands.
f) As a result, the volume of the liquid appears to have reduced.
g) Mark this reduced level of liquid as L₂.
h) On further heating, the thermal energy is supplied to the liquid through the container results in the expansion of the liquid.
i) Hence, the level of liquid rises to L₃
j) Now, the difference between the levels L₁ and L₃ is called apparent expansion. Apparent expansion = L₃ - L₁.
k) The difference between the levels L₂ and L₃ is called real expansion. Real expansion = L₃ - L₂.
Result:
The real expansion is always more than the apparent expansion.

(i) 0°C ice is colder than water.
(ii) This can be explained in terms of the latent heat of fusion (336 kJ) which is required to convert ice at 0°C to water at 0°C.
(iii) In simpler terms water at 0°C has higher heat content than ice at the same temperature.
(iv) Thus we conclude ice at 0°C is colder, from either of your hands.
(v) Then, you would felt more chillness on those hand, you kept ice at 0°C.